Ok, thanks to Opensourcer with finding this issue. Heres how to fix.
Extract the appimage
./Eddie --appimage-extract
Open squashfs-root/AppRun and comment out line 15
#rm $ARGV0
Download appimage tool for repacking
wget https://github.com/AppImage/AppImageKit/releases/latest/download/appimagetool-x86_64.AppImage
chmod +x appimagetool-x86_64.AppImage
Repack the appimage
path to/appimagetool-x86_64.AppImage /path to/squashfs-root
use this new appimage in gearlever
On launching Eddie, the file is no longer deleted.